Rewrite as a simplified fraction. ${2.3\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 236.6666...\\ 10x &= 23.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 213}$ ${x = \dfrac{213}{90}} $ ${x = \dfrac{71}{30}} \text{or} {2 \dfrac{11}{30}}$